Global warming and extreme climate have profoundly influenced our daily life in recent decades. They lead to many natural disasters, where landslide is one of the most severe ones. If a possible failure process of a landslide can be predicted in advance, an incident of such a disaster can be prevented accordingly. Understanding the post-failure behavior of a landslide becomes critical in slope stability assessment for disaster reduction. A successful prediction of a post-failure behavior provides useful information, including both kinematics and run-out distance. Warning given to the potentially vulnerable area may be issued before the incident to protect people’s lives and properties. (e.g., Guo et al., 2014; Yerro et al., 2019; Li et al., 2021)
Many numerical methods have been used to solve boundary value problems in geotechnical engineering. Limit equilibrium is a traditional method used for slope stability analyses. It is a fast and straightforward method with an assumption that materials are perfectly plastic. Force and/or moment equilibrium can be satisfied depending upon the method selected for each sliding surface. It reflects the slope’s limiting condition where the slope is about to fail. It also provides the so-called factor of safety associated with this slope failure. Researchers have commonly used the limit equilibrium to carry out slope stability analyses or back analysis to estimate soil parameters at the triggering of a landslide (e.g., Fredlund and Krahn, 1977; Duncan, 1996; Krahn, 2003).
Finite element method has been a widely used for decades, where the balance of forces and deformation continuity can be satisfied. Besides, constitutive models can be applied to mimic different material behaviors. Due to the anisotropic and inhomogeneous natures in geotechnical engineering, the finite element method is capable of simulating the process of a boundary value problem for a specific stress-strain relation. Duncan (1996) compared the limit equilibrium and the finite element methods for analyzing dams, embankments, and slopes. He showed the advantages and limitations of using the two methods in practical engineering problems. Troncone (2005) performed a landslide case using the limit equilibrium method (LEA) and finite element method (FEM). The analyzed result using the LEA showed that the average resistance along the sliding surface was between the peak resistance and residual resistance from laboratory tests. Using the LEA was found challenging to analyze the deformation and soil softening behavior of the translational type of landslides. In order to simulate a progressive failure process, an elasto-viscoplastic constitutive model implemented in the FEM was used.
Landslides are natural disasters with multiple processes in which the fluid and solid mechanisms should be taken into consideration simultaneously; therefore, Eulerian and Lagrangian approaches were introduced (Durst et al., 1984; Mostafa and Mongia, 1987; Tinti et al., 1999). The Eulerian approach is a fixed observation-only concerned with the fluid properties at a specific space and time point. It is capable of handling extreme deformation and avoiding mesh distortion. In the Lagrangian approach, the mesh is fixed to the material geometry and moves with the deformed material so large deformation may lead to mesh distortion. However, large deformation problems simulated by the finite element method normally require longer computational time and lead to convergence problems. Unified methods were then proposed to avoid the numerical difficulties on boundary setting and convective terms, and simulate large deformation problems without the constraint of mesh distortion. Cuomo et al. (2013) adopted a finite element method with a Eulerian mesh and Lagrangian integration points to model progressive failure of a landslide. Arbitrary Lagrangian Eulerian methods and coupled Eulerian-Lagrangian methods also belong to this kind (e.g., Donea et al., 2004; Henke et al., 2010; Chen et al., 2019).
Discontinuous approach, so-called the discrete element method and some meshless methods (e.g., smoothed particle hydrodynamics, the particle finite element method) were proposed for large deformation problems. These methods are applicable to track particle movements and analyze interactions at each contact point (e.g., Schwaiger and Higman, 2007; Bui et al., 2008; Nonoyama et al., 2015; Ceccato et al., 2018; Mao et al., 2020). This method is capable of understanding the failure mechanisms and the post-failure state after large deformation and the kinematic motion occur.
Material point method (MPM) can be considered as an extended version of finite element method in combination of computational fluid dynamics. This concept was first introduced by Sulsky et al. (1994). It is suitable for any large deformation problems, especially landslides, because it can simulate kinematics movement during sliding. In addition, excess pore pressure and effective stress can be determined and monitored during the entire failure process. Mirada Larroca (2015) used the MPM to evaluate the slip surface and the post-failure behavior of soil excavation. This method was compared with different numerical methods, including discrete element method and limit equilibrium method, through simulation of granular flows and moving landslides (Ceccato et al., 2018; Cuomo et al., 2019). More studies using the MPM have become more prevalent in numerical analysis (Chen et al., 2016; Llano-Serna et al., 2016; Soga et al., 2016; Wang et al., 2016; Cheng, 2018; Conte et al., 2019). The fundamental concept of the material point method is presented in Fig. 1. The computation process is demonstrated by a set of Lagrangian material points passing through the Eulerian mesh and delivering the information of their properties, mass, velocity, and acceleration to the nodes around them to have new updates during deformation. Furthermore, with assigned constitutive models in material points, stress-strain relations, stress paths, and excess pore pressure changes can be obtained during computation.
The aim of this study is to reproduce the possible failure scenario of a translational landslide in Taiwan using the MPM code Anura3D through back analysis. This case has been analyzed and simulated using LEA, FEM, FDM and DEM (e.g., Liao and Lee, 2011; Lee et al., 2013; Lee et al., 2016; Lo et al., 2016). The MPM has the advantage of analyzing the failure scenarios, where the runout distance and deposition at the post-failure stage can be determined. This landslide has been well documented in a complete forensic report with a detailed investigation, laboratory experiments, and numerical analyses (Liao and Lee, 2011).